A C0 discontinuous Galerkin formulation for Kirchhoff plates

A particular discontinuous Galerkin finite element formulation for the simulation of Kirchhoff plates is presented. It is rotation-free and utilises standard C0 Lagrange finite element basis functions, with the required continuity imposed in a weak sense across element boundaries. The implications of the scheme in terms of coercivity and convergence of the Galerkin problem in various norms are studied, with the formulation shown to be stable for any positive value of a penalty parameter. A priori error estimates are supported by a range of numerical examples. Properties of the approach for the important eigenvalue problems of plate buckling and vibration are also examined through numerical examples. Based on the results of the analysis and numerical examples, it is concluded that the formulation is robust, accurate and relatively simple.